Mastering GitHub Pages (Jekyll and GitHub Pages)

In this short note using the analogy with the recent resolution of the black hole information paradox we conjecture the order parameter for the state of consciousness based on the notion of the Page curve and the Page time. The entanglement between the state of the brain and time series of neuronal firing as well as the non-orthogonality of the functional connectomes play a key role.

Given any closed, connected, orientable $3$--manifold and integers $g\geq g(M), D > 0$, we show the existence of knots in $M$ whose genus $g$ bridge number is greater than $D$. These knots lie in a page of an open book decomposition of $M$, and the proof proceeds by examining the action of the map induced by the monodromy on the arc and curve complex of a page. A corollary is that there are Berge knots of arbitrarily large genus one bridge number.